It depends on what sort of defeat you're talking about. The problem for any TL posing Napoleonic victory is that Napoleon
cannot make a situation where the other powers of mainland Europe (Prussia, Austria, Spain, Russia) no longer hate him and wish to overthrow him, because of the way he treated them (i.e. utter arrogance, constantly demanding supplication and humiliating them all the time) and the fact that his personality made it inevitable for him to treat them in such a way. He certainly couldn't get any of them on his side with any degree of permanence, and his favoured solution was puppetisation, which isn't exactly very endearing to the nation being puppetised (see: his utter, utter failure in Spain). Plus, of course, his endless expansionism made everyone else very alarmed. As such, the UK could always muster up a coalition against Napoleon. None of his victories IOTL were really
permanent; those victories were essentially a case of his opponents agreeing to peace for the sake of taking a breather and preparing to fight him again.
One possible kind of Napoleonic victory is a successful invasion of Great Britain. That's… difficult, and it's not so simple as letting France achieve a major victory at Trafalgar (which itself isn't exactly trivial); you'd need rather more than that to get rid of the fact that to get rid of the fairly large numbers of British ships across the globe. Still, if it happens, then Napoleon can certainly enforce his will upon the UK… but if that
is the case, it will certainly be a case of enforcing will at the point of a bayonet and not of any British acquiescence, because there's no way the UK would tolerate such a move unless it had literally no choice at all and it's undoubtedly true that in such a situation the UK would find plenty of allies in mainland Europe outraged at Napoleon doing something even more offensive and outrageous to the dignity of legitimate monarchies (a popular artillery officer crowning himself as an emperor not, of course, being considered even remotely legitimate by them) than he ever did IOTL. So we'd be looking at a War of the Nth Coalition, if he tried this, a war that would only end if the UK suffered something at least as bad as Tilsit. Even at Tilsit Napoleon didn't do anything so extreme as to force members of the Prussian royal family into his bed (and the UK would
not regard it as a royal marriage, but as the Corsican Ogre forcing a British princess into his bed; they did
not view Napoleon as a true monarch); it's doubtful that Prussia would have accepted such terms without being completely overrun, and the same holds for the UK.
Another kind is the more "conventional" scenario where he manages to Tilsit-style weaken all his enemies in Western and Central Europe and prevent them from joining any future coalitions. That's probably still a recipe for a war against Russia at some point down the line once the Tsar feels ready to defy him, but that might be fairly late. In
this case, Napoleon's only hope of his regime's survival is if the Tsar chooses to fight Napoleon at a time of the Tsar's choosing, because if Napoleon attacks Russia at a time of Napoleon's choosing then his regime will suffer its OTL fate: the Russians withdrawing and thus taking advantage of his obsession with decisive battles and his inherent inability to "know when to fold 'em". If we presume that Napoleon's regime
does survive (as the OP seems to wish) then at some point, quite a lot of decades into the future, once animosity has died down, such a thing might be possible—so not with Charlotte and Napoleon I, but perhaps some future Hanover and some future Bonaparte.
Then there's what we might call the "uber" Napoleonic victory where he manages to subdue his enemies in Western and Central Europe
and invade and subdue Russia
and invade and subdue the UK. I think my tone alone expresses just how serious a possibility I think this is, so I shall leave it at that.
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As for the colonies of the UK/England, that, unlike the others, is pretty ASB. We'd see exactly the same thing as we saw with the Spanish colonies: people rebelling against the Napoleonic puppet regime (and only an utter Napoleonic puppet regime would permit a marriage between Napoleon and Charlotte: the submission of tolerating Napoleonic France's existence is one thing, such enormous and extreme submission is another) and going for either independence or even some kind of agreement with the previous, non-puppet regime (lots of the rebellions in Spanish America were originally pro-Bourbon and anti-Bonaparte, and only turned anti-Bourbon and republican due to the Bourbons' poor treatment of them). I'm pretty sure that the British forces in India would prefer joining the service of various Indian states than serving a French Empire that had chosen to humiliate the UK even more grievously than it chose to humiliate any European great power IOTL (except Spain and, depending on what you regard as a great power, the Netherlands), and that the British officers in North America would prefer even annexation by the USA, let alone a Brazilian-esque UK-in-exile in the Americas (which I would think is likelier), to submission to Napoleon. After all, many British generals IOTL were so pro-American that they actually refused to fight the Americans, whom they regarded as essentially British, in spite of the fact that the Americans didn't think so; somehow there wasn't
exactly that kind of sentiment with one of the most hated of all the UK's enemies in all its history.
So, broadly in summary: if Napoleon force the UK to give up Charlotte to him it can only be at the point of a bayonet. Because he is unable to rule the UK's colonies at a point of a bayonet, he will be unable to rule them.
That'll be it for today from me. Have a nice day.
